Macbook Pro Late 2015

Try connecting a wired USB keyboard to see if that makes any difference (you won't be able to perform an SMC Reset, but all other startup key options should work with a wired USB keyboard). It is possible the internal Trackpad IPD Flex Cable has failed which is a very common problem with the 2015 specifically.

You do need to hold the keys immediately after hearing the startup chime. Sometimes holding the keys before the startup chime may not allow the keys to be recognized. If you don't press & hold the keys soon enough after the startup chime, then you miss the window of opportunity for the keys to be recognized since the Retina models boot so much more quickly than older Macs.

Seems like the laptop has some sort of hardware issue which needs repaired. Make sure to have the power adapter connected in case you have a bad battery and make sure to disconnect all external devices.

Make sure you are using an 87W power adapter if you have the 15", or at least a 60W charger if it is a 13" model. Here is an Apple article for troubleshooting power adapter charging issues:

If your MagSafe cable or power adapter isn't working - Apple Support

Try an SMC Reset as well.

Even if using a power adapter, the battery could possibly still be causing a problem, but in reality it could be almost anything. A bad Logic Board is most likely, but a tech would need to physically examine & observe the laptop's behavior to make a better assessment.